That's really a question you need to ask of people who know about OE. A Microsoft user support form would be where I'd go for help.

OE is very old. So you must have XP? And is the computer itself equally old? I am surprised that if you run XP that you have been able to find a version of Thunderbird that is happy.

What I need to know is if thunderbird copies or moves the OE mail messages .

Thunderbird does not interfere with the inner workings of another email program. It asks that program for its stored messages, and works with what that other program gives it.

If the other program were to delete the messages (which seems rather unlikely) then that is its choice to do so and would be unaffected by Thunderbird or whatever program it is exporting its messages to.

I repeat my advice to find a forum where you can talk to people who know about OE. Ideally, that would be the authors, Microsoft, but I doubt you'll find any official forum that is prepared to offer support for a long-abandoned program such as OE.